SOLUTION: I am trying to help my son and am not sure. Please review the following: Write a system of lnear equations and solve. (substitution or elimination) The sum of two numbers is

Question 26924: I am trying to help my son and am not sure. Please review the following:
Write a system of lnear equations and solve. (substitution or elimination)
The sum of two numbers is 40. The difference of the two numbers is twice the smaller number. What are the numbers?

Answer by bmauger(101) (Show Source): You can put this solution on YOUR website!
As a story problem, this problem involves the often difficult step of translating from english to algebra. You will have two equations to solve for, the first coming from "The sum of two numbers is 40." We don't know anything about either number yet, so we'll call them x and y. And their sum is x+y, so we write for the first equation:
Eq 1:
The second equation talks about the difference of the two numbers. We don't know which one is bigger, but let's call x the big one and y the small one. Their difference then is "x-y" and "twice the small one" (y) is written "2y". Thus our second equation is:
Eq 2:
To solve using substitution first rewrite the Eq 1 getting x by itself:

Then substitute 40-y for x in the Eq 2:

Rearrange:

Divide:

Find x using the Eq 1:

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